This paper explains how to get integral representations for general hypergeometric series in one or several variables. The way is first to construct the so-called ``exponential modules'' lengthily studied in the \textit{B. Dwork's} book [Generalized hypergeometric functions (Oxford Press 1990; Zbl 0747.33001)] then to use a formal Laplace transform. The first step is shown to be equivalent to a construction of \textit{I. Gelfand}, \textit{N. Kapranov} and \textit{A. Zelevinsky} [Adv. Math. 84, 255-271 (1990; Zbl 0741.33011)]. More than half of the text is devoted to treating particular cases, namely Horn's list and Lauricella functions as well as \({}_ k F_{k-1}\). The confluent case is within the scope of the method whose only weakness is the lack of an easy computation for the cycle of integration. Here the authors impose that the ``parameters'' are algebraically independent but they claim that these conditions may be eliminated. Beyond the algebraic results given here, one knows that exponential modules enjoy useful \(p\)- adic properties such as Frobenius structure and that Boyarsky's principle is applicable to them. The paper is well and shortly written but not easy to read both because of numerous notations and rather computational proofs, and even some tedious computations of Dwork's book are used. In fact it can be viewed as a kind of introduction to this book.